Mutability, Conceptual Transformation, and Context Bradley C. Love Department of Psychology Northwestern University 2029 Sheridan Road Evanston, IL 60208
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Abstract Features differ in their mutability. For example, a robin could still be a robin even if it lacked a red breast; but it would probably not count as one if it lacked bones. I have hypothesized (Love & Sloman, 1995) that features are immutable to the extent other features depend on them. We can view a feature's mutability as a measure of transformational difficulty. In deriving new concepts, we often transform existing concepts (e.g. we can go from thinking about a robin to thinking about a robin without a red breast). The difficulty of this transformation, as measured by reaction time, increases with the immutability of the feature transformed. Conceptual transformations are strongly affected by context, but in a principled manner, also explained by feature dependency structure. A detailed account of context's effect on mutability is given, as well as corroborating data. I conclude by addressing how mutability-dependency theory can be applied to the study of similarity, categorization, conceptual combination, and metaphor.
1 Introduction: the importance of relations Cognitive scientists have begun to gain an appreciation that concepts (in the psychological sense) are more than independent sets of features. Any account of concept representation must address the relations that exist among features. Relations help explain why some features are more central to a representation, while others are easily transformable. For instance, relations among features explain why it is difficult to imagine a normal robin without a heart, while imagining a robin without a red breast is more plausible. Having a red breast is a mutable feature of robins, while having a heart is an immutable feature of robins. There have been varying accounts of why some features are relatively immutable, while others are mutable. On the theory-based view (e.g., Carey, 1985; Keil, 1989), the importance of the heart can be explained by appealing to a biological theory of how a robin functions. Such a theory would deem the heart central to our notion of what it means to be a normal robin, based on the web of relations in which the heart is embedded (e.g. "the heart pumps blood", "blood carries oxygen", "the brain needs oxygen", etc). The relations among features are labeled by the type of relation they represent (e.g. carries, pumps, needs). On this view (Murphy & Medin, 1985; Wellman, 1990), the concept robin coheres by virtue of the explanatory relations that hold
between its components (and perhaps those of other concepts). In contrast, the feature "has a red breast" does not play as critical of a role in the overall explanatory coherence of the concept robin, making the feature more mutable. That is, it is easy to imagine a robin not having a red breast (perhaps the robin has a brown breast). Not having a red breast does not have serious ramifications for a theory of what it means to be a robin. The story becomes more complex when we consider that the mutability of a feature can vary with context. For instance, in certain contexts, the feature "has a red breast" can become more immutable. If one is reminded or alerted to the mating purposes of having a red breast, the feature will become more immutable. Effectively, the context of mating highlights features with relations in common with the feature "has a red breast", making "has a red breast" more immutable. The effects of context on categorization and similarity ratings are well documented (Medin et. al., 1993). Context can facilitate the interpretation of noun-noun compounds, analogies, and nominative metaphors (Gerrig & Murphy, 1992; Gick & Holyoak, 1980; Gildea and Glucksberg, 1983).
2 The dependency stance: an implemented theory The theory-based view can explain why certain features are more critical or immutable, but the explanation has an ad hoc flavor and seems overly complex. It is unclear how a theory-based model could be implemented that predicts which features of a concept are mutable and which are immutable. It is difficult to see how qualitative statements like "plays a critical role in the overall explanatory coherence of the concept " can be made formal and yield quantitative predictions. The problem becomes more acute when we allow context to vary. Since relations among features are labeled by their type, it is not possible to employ a simple algorithm that calculates the importance of a feature, since different types of relations are not directly comparable. One could overcome this difficulty by employing a simpler representational scheme that still captured the basic intuitions of the theory-based view. I propose (Love & Sloman, 1995) that all types of relations can be collapsed to one primitive type, namely the unidirectional relation of depends; for the purposes of calculating feature mutabilities. In such a scheme, the
Beak Small
Feathers Eats
Red breast
Flies Moves
Two legs
Wings
Eats worms
Living
Lays eggs
Chirps Builds nests
Figure 1: The arrows point from a feature to one that it depends upon, as rated by subjects (Love & Sloman, 1995). relations pumps, carries, and needs would all be collapsed to the pairwise relation depends. Faced with the challenge of equating different types of relations, people may resort to using only dependency information in certain tasks. Figure 1 illustrates a dependency graph, in which relations among features are only represented as dependencies. Having many features depending upon a given feature will make it more difficult to transform the given feature since the transformation will disrupt the representation of the concept. Other features that depend upon the immutable feature will also change and this can have ramifications for the entire representation. For example, if you were told that a particular robin did not have wings, you would need to update your default assumption that the robin can fly, since "can fly" depends on "has wings". Performing conceptual transformations across mutable features is relatively easy because other features are unaffected by changes in mutable features. We would expect reaction time to be slower for transformations performed across immutable features. In experiment 1, I test this prediction. Having one type of relation makes it possible to compare all relations on the basis of magnitude. The mutability of a feature can be calculated by summing the number and strength of the other features that depend on it, which is a straightforward computation, yet accounts for subjects' mutability ratings (Love & Sloman, 1995). Obviously, there are tasks that require people to attend to the labels of relations, such as some reasoning tasks, but interestingly, such tasks require considerably more effort and processing time than tasks that do not demand labeled relations (Ratcliff & Mckoon, 1989). By positing that people employ a dependency-like representation, an explanation of how context affects perceived mutability is suggested. When forming a concept, one draws upon a huge database of knowledge, only using a fraction of it in forming any particular concept (Barsalou,
1993). An individual can conceive of a category in a number of different ways, depending on context and current goals. Studying these effects is critical to our understanding of concept representation as context can dictate which features are included in forming a concept. Since a feature is immutable to the extent that other features depend upon it, forming a concept from different sets of features (in different contexts) should affect feature mutability in a principled way. More precisely, if a feature is introduced (or highlighted) that depends upon a given feature, the given feature will become more immutable. Concretely, if I speak extensively of the mating practices of robins, and you know that certain aspects of the mating process depend upon the participants' color, then "has a red breast" should be more immutable in this context than in a context centered around flight.
3 Testing the dependency model Two studies were conducted to test the following predictions: i. Features rated as mutable should be easier to transform. Subjects should be faster at imagining derivative concepts that vary in a mutable feature than in a immutable feature. ; ii. This transformation is affected by context in a principled way explained by the dependency structure of the representation.
3.1 Experiment 1: Mutability as Transformation If subjects are performing a transformation of the concept robin to a derivative representation of robin when providing ratings for statements like, "How easily can you imagine a robin that does not have wings?", then one would expect that the ratings for such questions would correspond to the actual difficulty of the transformation. Furthermore, the difficult of a transformation should be measurable through
reaction time. Transformations of highly immutable features should take longer than transformations over mutable features. In experiment 1, I tested this prediction. Method Subjects. Subjects in the feature mutability rating task were 20 undergraduates from Brown University. They were paid for their participation. Subjects in the reaction time task were 20 undergraduates from Northwestern University. They received course credit in an introductory psychology course for their participation. Materials and procedure. The stimuli consisted of features from 4 categories (pine tree, robin, cucumber, and apple) taken from Dean and Sloman (1995). Mutability ratings were collected by having subjects answer questions like, "How easily can you imagine a robin without wings?" Subjects responded with a number between 0 and 1 that reflected the ease of the transformation. The number of features per category varied from 17 to 25. The 3 most mutable and immutable features from each category were chosen for the reaction time task, for a total of 24 features. Subjects were shown the name of the category and the feature on a Macintosh computer. They pressed the spacebar when they could imagine a member of the category not having the listed feature, but being normal in every other respect. To ensure that any difference in reaction time between mutable and immutable features could not be attributed to the goodness, accessibility, salience, or reading times of the features; a feature confirmation task was included as a control. The same stimuli were used with the addition of 24 distractors. Subjects were instructed to press "p" if the category had the given feature, and to press "q" if the category did not possess the feature. Since all the features of interest clearly belonged to their category, 32 distractor features that did not belong to the presented category were included to ensure that subjects would not be biased towards an affirmative response. Results All observations more than 3 standard deviations above the mean were discarded (the cutoffs were 14576 msecs for the imagining task, and 3341 msecs for the feature confirmation task). For analysis, reaction times were separated into two groups: mutable and immutable. Subjects took longer to imagine instances of a category varying in an immutable feature (t(539)=4.11, p )
B
7.37
C (no relation)
B
5.52
B (
